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mathematics | The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area R of that hemisphere? | [
"6/π",
"9/π",
"6",
"9",
"12"
]
| Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4 *PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
The answer is: D | D |
mathematics | If a farmer sells 5 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 10 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have? | [
"12",
"20",
"48",
"55",
"60"
]
| Say farmer has n goat and he is good for d days.:-
We have 3 equations given in question:-
(n-5) * d+4 =(n+10) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
10d-3n=30
4n-5d =20
=> n=20
Ans B it is!
The answer is: B | B |
mathematics | Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16?Which of the following Equation is NOT equivalent to 25x^2 = y^2 - 16? | [
"25x^2 + 4 = y^2",
"75x^2 = 3y^2 - 12",
"25x^2 = (y + 2)(y - 2)",
"5x = y - 4",
"x^2 = (y^2 - 4)/25"
]
| 1) Take the original equation and try to manipulate it so that it becomes 4 of the 5 answers
2) Take each answer choice and see if you can manipulate it to make it into the original equation.
With Answer D, we have...
5X = Y - 2
If we square both sides, we end up with....
(5X)^2 = (Y-4)^2
(5X)(5X) = (Y-4)(Y-4)
25X^2 = Y^2 - 8Y + 16
This is NOT a match for the original equation, so it's the answer that is NOT equivalent. D
The answer is: D | D |
mathematics | One-sixth of the attendees at a certain convention are female students, two-thirds of the attendees are female, and one-third of the attendees are students. If 250 of the attendees are neither female nor students, what is the total number of attendees at the convention? | [
"600",
"300",
"1200",
"1500",
"1600"
]
| Let no. of Attendee are A.
Now As per the condition of the problem stated above .
We have following population in the convention as Attendee.
Total no. of females = [2/3]*A
Total no. of females as student : [1/6]*A
Total no. of students = [1/3]*A
Total no. of male as student = [1/6]*A
Total no. of males = A - [2/3]*A = [1/3]A
No. of males which are not student = [1/3]A - [1/6]*A = 250
Hence A = 1500
Total no of males who are not student will be the answer as it states it should be neither female nor student
So Answer is D
The answer is: D | D |
mathematics | An express A starts at 2.30 pm from nampali station and travels towards vizag station at speed of 80 kmph. Another expressstarts at 4.30 pmfrom nampali station to vizag station at speed of 100 kmph. How far awayfrom station Nampali will the two trains meet?? | [
"600 km",
"700 km",
"750 km",
"800 km",
"900 km"
]
| Let train A take x hours to reach the point of meeting(let it be P)
Then train B will reach the same point in x-2 hours.
Distance covered to reach P by train A in x hours=Distance covered by B to reach P in x-2 hrs.
80*x=100(x-2)
80x=100x-200
x=10 hrs.
Distance from Nampali=x*speed of train A
=10*80
=800 km
ANSWER:D
The answer is: D | D |
mathematics | Two trains, each 100 m long, moving in opposite directions, cross other in 12 sec. If one is moving twice as fast the other, then the speed of the faster train is? | [
"76 km/hr",
"66 km/hr",
"40 km/hr",
"67 km/hr",
"22 km/hr"
]
| Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/12 = 3x => x = 50/9
So, speed of the faster train = 100/9 = 100/9 * 18/5 = 40 km/hr.
Answer:C
The answer is: C | C |
mathematics | If 4a = 16b and 9b = 11c, Find a:b:c? | [
"52:13:7",
"44:11:9",
"7:13:52",
"7:13:54",
"None of these"
]
| Explanation:
(4a = 16b ==> a/b = 16/4)
and (9b = 11c ==> b/c = 11/9)
==> a:b = 16:4 and b:c = 11:9
a:b:c = 44:11:9
Answer: Option B
The answer is: B | B |
mathematics | The C.P of 10 pens is equal to the S.P of 16 pens. Find his gain % or loss%? | [
"loss 16 2/8%",
"loss 16 6/3%",
"loss 16 2/3%",
"loss 18 2/3%",
"loss 37.5%"
]
| 10 CP = 16 SP
16 --- 6 CP loss
100 --- ? => 37.5% loss
Answer:E
The answer is: E | E |
mathematics | A table is bought for Rs.800/- and sold at a loss of 10% find its selling price | [
"s.500/-",
"s.530/-",
"s.540/-",
"s.600/-",
"s.720/-"
]
| 100 % ------> 800 (100 * 8 = 800)
90 % ------> 720 (90 * 8 = 720)
Selling price = Rs.720/-
E
The answer is: E | E |
mathematics | If there are 200 questions in a 3 hr examination. Among these questions are 100 type A problems, which requires twice as much as time be spent than the rest of the type B problems. How many minutes should be spent on type A problems? | [
"72 min",
"62 min",
"70 min",
"74 min",
"120 min"
]
| x=time for type B prolems
2x=time for type A problem
total time=3hrs=180min
100x+100*2x=180
x=180/300
x=0.6
time taken for type A problem=100*2*0.6=120min
ANSWER:E
The answer is: E | E |
mathematics | A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 2 min, then the length of the tunnel is? | [
"2898",
"1800",
"500",
"297",
"435"
]
| Speed = 78 * 5/18 = 65/3 m/sec.
Time = 2 min = 120 sec.
Let the length of the train be x meters.
Then, (800 + x)/120 = 65/3
x = 1800 m.
Answer: B
The answer is: B | B |
mathematics | Jack has two dice, one has six equally probable sides, labeled 1, 2, 3, 4, 5, 6, and the other has seven equally probable sides, labeled 1, 2, 3, 4, 5, 6, 7. If Jack rolls both dice what is the probability that both of the numbers will be 7? | [
"3/14",
"1/7",
"0",
"1/2",
"12/21"
]
| METHOD-1
Probability that the number on first die is 7 = 0
Probability that the number on Second die is 7 = 1/7 [Because 1 out of 7 faces is 7]
Probability that Both Dice result in odd numbers = (0)*(1/7) = 0
Answer: Option C
The answer is: C | C |
mathematics | 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work? | [
"127 days",
"667 days",
"177 days",
"187 days",
"225 days"
]
| 1 man's 1 day work = 1/100
(10 men + 15 women)'s 1 day work = 1/6
15 women's 1 day work = (1/6 - 10/100) = 1/15
1 woman's 1 day work = 1/225
1 woman alone can complete the work in 225 days.
Answer:E
The answer is: E | E |
mathematics | 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 10 pumps work to empty the tank in 1 day? | [
"4.8",
"3.6",
"1.1",
"1.2",
"1.3"
]
| 3 pumps take 16 hrs total (8 Hrs a day)
If 1 pump will be working then, it will need 16*3=48 hrs
1 pump need 48 Hrs
If I contribute 10 pumps then
48/10=4.8 hrs.
answer :A
The answer is: A | A |
mathematics | The length of rectangle is thrice its breadth and its perimeter is 88 m, find the area of the rectangle? | [
"432 sq m",
"363 sq m",
"452 sq m",
"428 sq m",
"525 sq m"
]
| 2(3x + x) = 88
l = 33 b = 11
lb = 33 * 11 = 363
ANSWER:B
The answer is: B | B |
mathematics | Shekhar started a business investing Rs.25,000 in 1999.In 2000,he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000.In 2001,Shekhar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000.What will be Rajeev’s share in the profit of Rs.1,80,000 earned at the end of 3 years from the start of the business in 1999 ? | [
"Rs.45,000",
"Rs.60,000",
"Rs.70,000",
"Rs.75,000",
"None of these"
]
| Solution
Shekhar : Rajeev : Jatin
= (25000x12+35000x12+45000x12) :(35000x24) : (35000x12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
∴ Rajeev’s share = Rs.(18000x2/6) = Rs. 60,000. Answer B
The answer is: B | B |
mathematics | 1,5,6 ,25, 26,30,31, 125,126,130,131,150,151,155,156,……… What is the value of 33rd term in the
given series | [
"3124",
"3125",
"3126",
"3127",
"3128"
]
| 1st terms gives 2nd and 3rd terms
1st term is 1
2nd term 1*5=5 3rd term= 5+1=6
similarly,
4th term =5*5=25 5th term=25+1=26
1st term gives 2nd and 3rd values
2nd term gives 4th and 5th values
lke wise
16th term gives 32nd and 33rd values
16 th term is 125*5=625
32nd term is 625*5=3125 and 33rd value is 3126
ANSWER:C
The answer is: C | C |
mathematics | Find the number of square tiles to cover the floor of a room measuring 6.5 m * 8.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? | [
"768",
"476",
"429",
"428",
"413"
]
| Floor area to be covered by tiles = 6 * 8 = 48
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 48/0.0625 = 768
Answer : A
The answer is: A | A |
mathematics | A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train? | [
"79.7",
"79.8",
"76.2",
"79.2",
"29.2"
]
| Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5
= 79.2 km/hr.
Answer:D
The answer is: D | D |
mathematics | If 213 × 16 = 3408, then 1.6 × 21.3 is equal to : | [
"0.3408",
"3.408",
"34.08",
"340.8",
"None of these"
]
| Solution
1.6 × 21.3 = (16/10x 213/10)= (16x 213/100) = 3408/100 = 34.08. Answer C
The answer is: C | C |
mathematics | Find the sum The difference between the compound and S.I. on a certain sum of money for 2 years at 10% per annum is Rs. 100 of money? | [
"1500",
"6000",
"2500",
"1400",
"2000"
]
| P = 100(100/10)2 => P = 2000
Answer: E
The answer is: E | E |
mathematics | y = 248 - 198x
Which of the following values of x gives the greatest value of y in the equation above? | [
"200",
"100",
"0.5",
"-5",
"4"
]
| Clearly, the negative value of x will result in maximum value of y.
Don't even look at the rest of the answer choices as only one negative value is being present.
Answer is D
The answer is: D | D |
mathematics | At 1:00, Annie starts to bicycle along a 84 mile road at a constant speed of 14 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet? | [
"2:30",
"3:00",
"4:00",
"5:00",
"6:00"
]
| In the first 30 minutes, Scott can travel 6 miles, so there are 78 miles left.
Together Annie and Scott can complete 26 miles.
78/26 = 3, so they will meet 3 hours after 1:00.
The answer is C.
The answer is: C | C |
mathematics | A and B go around a circular track of length 600 m on a cycle at speeds of 24 kmph and 60 kmph. After how much time will they meet for the first time at the starting point? | [
"120 sec",
"176 sec",
"178 sec",
"180 sec",
"189 sec"
]
| Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (24 * 5/18) , 600/ (60 * 5 /18) }
=180 sec.
Answer: D
The answer is: D | D |
mathematics | A train 350 m long, running with a speed of 63 km/hr will pass a tree in? | [
"22 sec",
"16 sec",
"17 sec",
"88 sec",
"20 sec"
]
| Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 350 * 2/35 = 20 sec
Answer:E
The answer is: E | E |
mathematics | A freight elevator can carry a maximum load of 1100 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator? | [
"59",
"85",
"190",
"215",
"210"
]
| The average of existing 2 package is150 + 280/2 = 430/2 = 215
Remaining allowed weight = 1100 - 200 - 430 = 470.
allowed per package = 470 / 3 = 156
So difference in average of existing and allowable = 215 - 156 = 59
Hence A
The answer is: A | A |
mathematics | Five bells begin to toll together at 12:00 noon and toll respectively at intervals of 4, 5, 6, 8, and 9. seconds. Not including the toll at 12:00 noon, how many more times will all five bells toll together before 3:01 pm (i.e. three hours and one minute later)? | [
"25",
"30",
"35",
"40",
"45"
]
| The least common multiple is 2*2*2*3*3*5=360.
10860 seconds / 120 = 30 + remainder.
The answer is B.
The answer is: B | B |
mathematics | If b < 3 and 3x - 3b = 0, which of the following must be true? | [
"x > -3",
"x < 2",
"x = 3",
"x < 3",
"D. x > 3"
]
| 3x - 3b = 0
Therefore, 3x = 3b
As, b<3
3x < 3(3)
i.e x < 3
Answer : D
The answer is: D | D |
mathematics | A husband and wife can complete a certain task in 1 and 2 hours respectively. Their children, Rae and Herman, can complete the same task in 4 and 5 hours, respectively. What is the ratio of the couple's time working together to complete the task to the children's time working together to complete the task? | [
"a)15:46",
"b)3:10",
"c)12:23",
"d)5:18",
"e)10:3"
]
| couples one hour work=1/1+1/2=3/2
so total time=2/3..
now, kids one hour work=1/4+1/5=9/20
so total time=20/9..
ratio=2/3:20/9=3/10
ans B
The answer is: B | B |
mathematics | -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 4 greater than the preceding term. Which of the following could not be a term in the sequence? | [
"0",
"200",
"440",
"668",
"762"
]
| Simplifying the question into easier words we just need to find which of the numbers is not divisible by 4
clearly the answer is 762 because if we divide 762 by 4 we get a remainder of 2
Correct answer - E
The answer is: E | E |
mathematics | In 1990 a total of 100 earthquakes occurred worldwide, some but not all of which occurred in Asia. If 20 of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia? | [
"1/7",
"1/6",
"1/2",
"1/4",
"1/3"
]
| We're given a couple of facts to work with:
1) There were a total of 100 earthquakes
2) Of those earthquakes, 20 of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Thus, there were 80 earthquakes that DID NOT occur in Asia....
The answer to the question is 20/80 ie. 1/4
Answer : D
The answer is: D | D |
mathematics | A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%? | [
"600",
"729",
"278",
"268",
"308"
]
| Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
The answer is: A | A |
mathematics | Four angles of a quadrilateral are in G.P. Whose common ratio is an intiger. Two of the angles are acute while the other two are obtuse. The measure of the smallest angle of the quadrilateral is | [
"12",
"24",
"36",
"46",
"52"
]
| Let the angles be a, ar, ar 2, ar 3.
Sum of the angles = a ( r 4- 1 ) /r -1 = a ( r 2 + 1 ) ( r + 1 ) = 360
a< 90 , and ar< 90, Therefore, a ( 1 + r ) < 180, or ( r 2 + 1 ) > 2
Therefore, r is not equal to 1. Trying for r = 2 we get a = 24
Therefore, The angles are 24, 48, 96 and 192.
ANSWER:B
The answer is: B | B |
mathematics | In a colony of 70 residents, the ratio of the number of men and women is 5: 2. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony? | [
"A)1:5",
"B)1:1",
"C)1:8",
"D)1:9",
"E)1:3"
]
| Number of men in the colony = 5/7 * 70 = 50.
Number of women in the colony = 2/7 * 70 = 20.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 50 - 10 = 40.
Number of educated men and uneducated men are in the ratio 10 : 40 i.e., 1:4.
Answer:A
The answer is: A | A |
mathematics | If y exceeds x by 20%, then x is less than y by? | [
"16%",
"16 1/3 %",
"16 2/3 %",
"16 3/5 %",
"None of these"
]
| Explanation:
X=100 y=120
120------20
100-------? => 16 2/3%
ANSWER IS C
The answer is: C | C |
mathematics | A man can row downstream at 18 kmph and upstream at 12 kmph. Find the speed of the man in still water and the speed of stream respectively? | [
"3",
"5",
"6",
"4",
"9"
]
| Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 12 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 3. Answer: A
The answer is: A | A |
mathematics | The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8800. If his salary for the month of May is Rs.6500, find his salary for the month of January? | [
"s.3300",
"s.4570",
"s.4500",
"s.4550",
"s.2500"
]
| Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8800
= 35200 ----(2)
(2)-(1) i.e. May - Jan = 3200
Salary of May is Rs.6500
Salary of January = Rs.3300
Answer:A
The answer is: A | A |
mathematics | The jogging track in a sports complex is 627 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in? | [
"4.56 min",
"5.28 min",
"5.08 min",
"9.28 min",
"5.988 min"
]
| Clearly, the two will meet when they are 627 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 627 m apart, they take (100/825 * 627/1000) hrs = (627/8250 * 60) min = 4.56 min.
Answer: A
The answer is: A | A |
mathematics | A 260 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train ? | [
"240 mts",
"270 mts",
"260 mts",
"250 mts",
"280 mts"
]
| Explanation:
Relative speed = 120 + 80 = 200 km/hr.
= 200 x 5/18 = 500/9 m/sec.
Let the length of the other train be L mts.
Then, (L + 260)/9 = 500/9 => L = 240 mts.
ANSWER IS A
The answer is: A | A |
mathematics | Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements X are possible? | [
"30",
"60",
"90",
"180",
"540"
]
| 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements X including the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X-- Y-- Z
12-- 34-- 56
12-- 56-- 34
34-- 12-- 56
34-- 56-- 12
56-- 12-- 34
56-- 34-- 12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..C
The answer is: C | C |
mathematics | Rohit and Rohan can complete a work in 12 days and 6 days respectively. How much time will they take when working together? | [
"4",
"3",
"5",
"2",
"1"
]
| Time taken by Rohit and Rohan = xy/ x+y
=12*6/(12+6)
= 4 days
ANSWER:A
The answer is: A | A |
mathematics | If the money was put in for the same duration of time by A,B and C, three business partners and four times A’s capital is equal to 6 times B’s capital is equal to 10 times C’s capital. Determine that out of a total profit of Rs 4650 what is C’s share? | [
"Rs 9008",
"Rs 906",
"Rs 900",
"Rs 905",
"Rs 901"
]
| Explanation:
It is given that business partnership is independent of time in this case as all the investors have invested their money for same amount of time.
Let A’s capital be x, B’s capital be y and C’s capital be z.
=>x+y+z = 4650
=> 4x = 6y = 10z
=>C’s share is z so let us solve the question w.r.t. z
=>x = 5z/2
=>y = 5z/3
=>(5z/2)+(5z/3)+(z) = 4650
=>31z = 4650*6
=>z = 900
ANSWER:C
The answer is: C | C |
mathematics | Which of the following is not the square of an integer? | [
"275625",
"385641",
"426437",
"532900",
"318096"
]
| The square of an integer (n^2) can have only the following units digit:
0, if the units digit of n is 0;
1, if the units digit of n is 1 or 9;
4, if the units digit of n is 2 or 8.
5, if the units digit of n is 5;
6, if the units digit of n is 6 or 4;
9, if the units digit of n is 3 or 7.
The square of an integer cannot have the units digit of 2, 3, 7, or 8.
The answer is C.
The answer is: C | C |
mathematics | At what time between 5 and 6 o' clock are the hands of a 3 minutes apart ? | [
"24",
"55",
"66",
"88",
"21"
]
| In this type of problems the formuae is
(5*x+ or - t)*12/11
Here x is replaced by the first interval of given time. Here x is 5.
t is spaces apart
Case 1 : (5*x + t) * 12/11
(5*5 + 3) * 12/11
28 * 12/11 = 336/11= min
therefore the hands will be 3 min apart at 31 5/11 min past 5.
Case 2 : (5*x - t) * 12/11
(5*5 -3 ) * 12/11
22 *12/11 = 24 min
therefore the hands will be 3 min apart at 24 min past 5
Answer: A) 24min
The answer is: A | A |
mathematics | Right triangle PQR is to be constructed in the xy-plane so that the right angle is at P and PR is parallel to the x-axis. The x and Y coordinates of P,Q and R are to be integers that satisfy the inequalitites -4≤ X≤ 5 and 6≤ y≤ 16. How many different triangles with these properties could be constructed? | [
"110",
"1100",
"9900",
"10000",
"12100"
]
| total values for x=10;y=11
x1,y1=10*11.......................coordinates of 1st pnt
x2,y2=9*1(y2=y1)............... coordinates of 2nd pnt y coordinates will be same as that of 1st pnt bcoz it is parallel to x axis
x3,y3=1*10(x2=x3)..........coordinates of 3rd pt. x coordinates will be same as that of 2nd point bcoz to make a right angle it has to be parallel to y axis
tot ways=10*11*9*1*1*10=9900
ANS:C
The answer is: C | C |
mathematics | In how many ways can 11 books on English and 9 books on French be placed in a row on a shelf so that two books on French may not be together? | [
"220.",
"240",
"260",
"280",
"300"
]
| We have 11 English and 9 French books, no French books should be adjacent.
Imagine 11 English books in a row and empty slots like below:
*E*E*E*E*E*E*E*E*E*E*E*
Now if 9 French books would be placed in 12 empty slots, all French books will be separated by English books.
So we can "choose" 9 empty slots from 12 available for French books, which is 12C9=220. ANS:A
_________________
The answer is: A | A |
mathematics | In a bag there are a certain number of red balls and blue balls. The probability of picking up exactly 1 blue ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of red balls to blue balls in the bag | [
"5:1",
"1:6",
"1:4",
"1:46",
"1:1"
]
| since the probability of drawing a blue ball out of two picks is 1/2.
the ratio of the blue ball to red balls should be 1:1
Answer : E
The answer is: E | E |
mathematics | There are some pigeons and hares in a zoo. If heads are counted, there are 100. If legs are counted, there are 580. The number of hares in the zoo is? | [
"210",
"182",
"190",
"137",
"371"
]
| 100*2 = 200
580
-----
380
1----2
?----380 = 190
Answer:C
The answer is: C | C |
mathematics | If a, b, and c are integer and ab + c is odd, which of the must be true?
I. a + c is odd
II. b + c is odd
III. abc is even | [
"I only",
"II only",
"III only",
"I and III only",
"II and III only"
]
| Personally I'd approach this question in another way.
ab+c=odd, means:
1. ab=even (which means that at least one of them is even) and c=odd
OR:
2. ab=odd (which means that both are odd) and c=even
We can see that in both cases at least one is even thus option III (abc=even) is always true.
Now, for I: if c=odd(case 1) and a=odd(so b=even) then a+c=even≠odd, so this option is not always true.
Exactly the same for option II: if c=odd (case 1) and b=odd (so a=even) then b+c=even≠odd, so this option is not always true.
Answer: C (III only).
The answer is: C | C |
mathematics | Heinz produces tomato puree by boiling tomato juice. The tomato puree has only 20% water while the tomato juice has 90% water. How many liters of tomato puree will be obtained from 40 litres of tomato juice? | [
"2.8 liters.",
"2.5 liters.",
"5 liters.",
"2.6 liters.",
"2.1 liters."
]
| Answer:
Explanation:
In each of the solutions, there is a pure tomato component and some water. So while boiling, water evaporates but tomato not. So we equate tomato part in the both equations.
⇒⇒ 10%(40) = 80%(x)
⇒⇒ x = 5 liters.
Answer:C
The answer is: C | C |
mathematics | if 50% of (x-y) = 20% of (x+y) then what percent of x is y? | [
"2.5%",
"10%",
"5%",
"15%",
"43%"
]
| 50% of (x-y)=20% of(x+y)
(50/100)(x-y)=(20/100)(x+y)
5(x-y)=2(x+y)
3x=7y
x=7/3y
therefore required percentage
=((y/x) X 100)% = ((y/(7/3)y) X 100) =43%
Answer is E.
The answer is: E | E |
mathematics | Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums? | [
"30",
"36",
"70",
"80",
"150"
]
| Jane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Jane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Jane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
Answer B
The answer is: B | B |
mathematics | Tough and Tricky questions: Word Problems.
It takes Sarah 44 minutes to do one oil change, and it takes Alice 20 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously? | [
"10:00 a.m.",
"10:42 a.m.",
"12:00 a.m.",
"12:40 p.m.",
"2:00 p.m."
]
| LCM of 2044
20 = 2 * 2 * 5
44 = 2 * 2 * 11
LCM = 2 * 2 * 5 * 11 = 220 = 3 hour 40 minutes
1240PM
D
The answer is: D | D |
mathematics | A straight pipe 1 yard in length was marked off in halves and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard? | [
"1/6 and 1/4 only",
"1/6 and 1/3 only",
"1/6, 1/4, and 1/3",
"1/12, 1/6 and 1/4",
"1/12, 1/6, and 1/3"
]
| Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 2th : 0/2, 1/2, 2/2
and 3rd : 0/3, 1/3, 2/3, 3/3
Now with understood common denominator 6 write the numbers : for 2th : 0,3,6 and for 3rd : 0,2,4,6
Now comine : 0,2,3,4,6
Now find the cut with denominator 6 (Substracrt adjacent terms : 1/3, 1/6, 1/6, 1/3 i.e. 1/3 and 1/6 after removing duplicates.
answer : B
The answer is: B | B |
mathematics | Anthony and Cindy were each given x dollars in advance to perform at a community festival. Anthony eventually performed on all 14 days of the festival, while Cindy performed on 5 fewer days than Anthony performed. If Cindy gives Anthony y dollars of her advance payment so that they would have each received the same daily rate, what was Anthony paid in advance, in terms of y? | [
"2y",
"4y",
"23/5y",
"6y",
"10y"
]
| Anthony performed for 14 days meansw Cindy performed for(14-5)=9 days.
If Cindy gives y dollars to Anthony their Daily rate will be equal.It means
(x+y)/14=(x-y)/9
Solving we get, x=23/5y
Now Anthony's Advance is x=23.5y .So answer should be C.
The answer is: C | C |
mathematics | A rectangular floor measures 2 by 3 meters. There are 5 white, 5 black, and 5 red parquet blocks available. Each block measures 1 by 1 meter. In how many different f colors patterns can be floor be parqueted? | [
"104",
"213",
"3^5",
"705",
"726"
]
| Total number of squares we need to fill = 6
Number of colors we have f= 3
Therefore, total number of patterns = 3*3*3*3*3*3 = 729
However, this is considering that we can have a case in which all tiles are the same color. Since we are given that the quantity of each tile is 5 and the number of tiles required is 6, we know that this case cannot be possible. Therefore we must subtract the cases in which all tiles will be of the same color (3 cases since there are 3 colors).
Thus our answer should be :729 - 3 = 726
Answer : E
The answer is: E | E |
mathematics | A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 10 days before the completion of the work. In how many days was the work completed? | [
"12.5 days",
"16 days",
"18 days",
"11 days",
"38 days"
]
| One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 10 days = 10*(1/24 + 1/30) = 3/4
Remaining work = 1/4
The number of days required for this initial work = 2.5 days.
The total number of days required = 10 + 2.5 = 12.5 days.
Answer: A
The answer is: A | A |
mathematics | what is the unit digit in [(6273)^1793x(625)^317x(341)^491]? | [
"0",
"2",
"3",
"5",
"None of them"
]
| Unit digit in (6374)^1793=Unit digit in (4)^1793
=Unit digit in [(4^2)^896 x 4]
=Unit digit in (6x4)=4
Unit digit in (625)^317=Unit digit in (5)^317=5
Unit digit in (341)^491=Unit digit in (1)^491=1
Required digit = Unit digit in (4x5x1)=0
Answer is 0
The answer is: A | A |
mathematics | If 2^z is a factor of 24!, which of the following could be the value of z?
I. 22
II. 23
III. 24 | [
"I only",
"II only",
"I and II",
"I, II, and III",
"None"
]
| 24! contains all numbers from 1 to 24. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 12
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 22
The answer is A.
The answer is: A | A |
mathematics | Calculate the value of u: 16u^2-7u+2 = 125 | [
"5",
"2",
"4",
"1",
"3"
]
| Using the elimination method substitute options for x and find the correct option.
Answer: E
The answer is: E | E |
mathematics | For an upcoming charity event, a male vocalist has agreed to sing 5 out of 8 “old songs” and 3 out of 7 “new songs.” How many ways can the singer make his selection? | [
"25",
"50",
"150",
"217.78",
"600"
]
| =8C5*7C3
=8*7/3*7*5/3
=217.78
Ans = D
The answer is: D | D |
mathematics | In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg? | [
"7:3",
"3:7",
"4:6",
"5:7",
"8:9"
]
| Required rate = 3.50 : 1.50 = 7 : 3.
ANSWER A
The answer is: A | A |
mathematics | All factors of a positive integer X are multiplied and the product obtained is X^3. If X is greater than 1, how many factors does X have? | [
"2",
"3",
"4",
"5",
"6"
]
| The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.
For example,
Factors of 6: 1, 2, 3, 6
1 has a complementary factor 6 such that 1*6 = 6 (the original number)
2 has a complementary factor 3 such that 2*3 = 6 (the original number)
So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).
So if you know that the product of all factors is X^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.
E)
The answer is: E | E |
mathematics | If 0 < x < 1 < y, which of the following must be true? | [
"1 < 1/x < 1/y",
"1/x < 1 < 1/y",
"1/x < 1/y < 1",
"1/y < 1 < 1/x",
"1/y < 1/x < 1"
]
| Soln:
0<x<1<y. Let x=1/2 and y =2
Substituting values:
A. 1<2<1/2 --- Wrong
B. 2<1< 1/2 --- Wrong
C. 2<1/2<1 --- Wrong
D. 1/2<1<2 --- Correct
E. 1/2<2<1 --- Wrong
Hence answer is D
The answer is: D | D |
mathematics | X starts a business with Rs.45000. Y joins in the business after 3 months with Rs.30000. What will be the ratio in which they should share the profit at the end of the year? | [
"1:2",
"2:1",
"1:3",
"3:1",
"4:2"
]
| Explanation:
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
=45000×12:30000×9=45×12:30×9=3×12:2×9=2:1
ANSWER IS B
The answer is: B | B |
mathematics | if the annual rate of simple interest increases from 10% to 12.5% .Then a man’s yearly income from an investment increases by Rs.1250. His principle amount is: | [
"Rs,45000",
"Rs.50,000",
"Rs. 60,000",
"Rs.65,000",
"Rs.75,000"
]
| Let the sum be Rs.x Then, (x*25/2*1/100) – (x*10*1/100)= 1250
25x-20x = 250000 ;
x=50000
ANSWER:B
The answer is: B | B |
mathematics | CP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each? | [
"$9,500",
"$10,500",
"$11,500",
"$12,000",
"$12,500"
]
| Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = $17,500
C.P of 1st buffalo = $17,500
C.P of 2nd buffalo = 30,000 - 17,500 = $12,500
E
The answer is: E | E |
mathematics | If you flip a coin three times, what is the probability that you will get three heads? | [
"1/4",
"1/5",
"1/6",
"1/7",
"1/8"
]
| The probability of getting heads on a single flip is 1/2,
The probability of getting heads on each flip is P_1st * P_2nd * P_3rd,
Thus, P = (1/2)^3 = 1/8.
Answer = E
The answer is: E | E |
mathematics | A shipment of 8 TV sets contains 6 black and white sets and 2 color sets. If 2 TV sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black and white set? | [
"1/7",
"1/4",
"5/14",
"11/28",
"27/28"
]
| 2/8 * 1/7 = 2/56
1-(2/56) = 54/56 = 27/28
Answer E
The answer is: E | E |
mathematics | A young girl counted in the following way on the fingers of her left hand. She started collang the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little finger 5, then reversed direction calling the ring finger 6, the the middle finger 7, the index finger 8, the thumb 9 then back to the index finger for 10, the middel finger for 11, and so on. She counted up to 1995. She ended on her | [
"a) thumb",
"b) the index finger",
"c) the middle finger",
"d) the ring finger",
"e) the little finger"
]
| Notice the pattern. The thumb lansd up at numbers 1,9,17,25,33,... so every 8th number
By this patter the thumb is also at number 1993 (multiple of 8 + 1)
Hence 1995 has to be the middle finger
Answer is (C)
The answer is: C | C |
mathematics | A certain automobile company’s best-selling model is the Speedster. The Speedster, like all of their other models, comes in coupe and convertible styles. 2/3 of the current inventory is Speedsters, of which 4/5 are convertibles. If there are 40 vehicles that are not Speedsters, how many Speedster convertibles are there? | [
"30",
"64",
"60",
"70",
"90"
]
| Total Vehicle = 2/3 of speedster + 1/3 of others.
Speedster convertibles = 2/3 total vehicle * 4 /5
Given : 1/3 constitutes 40 Vehicles. hence 2/3 constitutes 80
Speedster convertibls = 80 * 4/5 = 64
B
The answer is: B | B |
mathematics | A container contains a dry mixture of sand and stones. Mass of sand and stones in the container is in the ratio 1:3. If 12 kg sand is added to the container, the ratio of masses of sand and stones becomes 5:3. Originally, how much more was the mass of stones than sand in the container? | [
"12",
"9",
"6",
"3",
"1"
]
| Suppose originally the mass of sand in the container was x. So the mass of stones, originally, would be 3x because mass of sand and stones in the container is in the ratio 1:3.
If 12 kg sand is added, mass of sand becomes x + 12, and the mass of stones remains unchanged. But now the ratio of the mass of sand and stones is 5:3.
This means,
(x + 12)/3x = 5/3, which gives x = 3.
So originally, there was 3 kg sand and 9 kg stones.
So, the mass of stones was 6 kg more than the mass of sand.
Ans C
The answer is: C | C |
mathematics | What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage? | [
"92.9",
"96.3",
"92.2",
"96.7",
"92.8"
]
| Explanation:
Use the formula,
CP= 100 – discount + brokerage%
CP= 100-8+1/5
92.2
Thus the CP is Rs 92.2.
ANSWER: C
The answer is: C | C |
mathematics | The least common multiple of positive integer w and 3-digit integer n is 690. If n is not divisible by 3 and w is not divisible by 2, what is the value of n? | [
"115",
"230",
"460",
"575",
"690"
]
| The LCM of n and w is 690 = 2*3*5*23.
w is not divisible by 2, thus 2 goes to n
n is not divisible by 3, thus 3 goes to w.
From above:
n must be divisible by 2 and not divisible by 3: n = 2*... In order n to be a 3-digit number it must take all other primes too: n = 2*5*23 = 230.
Answer: B.
The answer is: B | B |
mathematics | If xerox paper costs 5 cents a sheet and a buyer gets 10% discount on all xerox paper one buys after the first 200 papers and 20% discount after first 1000 papers, how much will it cost to buy 2500 sheets of xerox paper? | [
"$125",
"$106",
"$135",
"$90",
"$100"
]
| 30 sec approach - solve it using approximation
2500 sheet at full price, 5 cent = 125
2500 sheet at max discount price, 4 cent = 100
Your ans got to be between these two.
Ans B it is.
The answer is: B | B |
mathematics | Which of the following numbers is two more than the square of an odd integer? | [
"14,173",
"14,361",
"15,253",
"15,737",
"16,131"
]
| If a square has an odd unit's digit, then its ten's digit must be even.
Only 16,131-2 = 16,129 satisfies this condition.
The answer is E.
The answer is: E | E |
mathematics | A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going? | [
"15",
"61",
"21",
"14",
"12"
]
| Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [385 * 3/55] sec = 21 sec
Answer: C
The answer is: C | C |
mathematics | The wheel of a motorcycle, 70 cm in diameter makes 40 revolutions in every 10 seconds. What is the speed of the motorcycle in km/hr | [
"30.68 km/hr",
"31.68 km/hr",
"32.68 km/hr",
"33.68 km/hr",
"None of these"
]
| Explanation:
In this type of question, we will first calculate the distance covered in given time.
Distance covered will be, Number of revolutions * Circumference
So we will be having distance and time, from which we can calculate the speed. So let solve.
Radius of wheel = 70/2 = 35 cm
Distance covered in 40 revolutions will be
40 * Circumference =40 * 2*\pi*r =40∗2∗22/7∗35=8800cm
=8800/100m=88m
Distance covered in 1 sec =88/10=8.8m
Speed=8.8m/s=8.8∗18/5=31.68km/hr
Option B
The answer is: B | B |
mathematics | In a span of 24 hours, how many times would the two hands of a clock point exactly in opposite directions ? | [
"10",
"11",
"23",
"22",
"24"
]
| Explanation:
In every hour, the two hands (minute and hour) of the clock would be exactly opposite to each other once. But, from 5 o'clock to 6 o'clock and from 6 o'clock to 7 o'clock (a span of hours), they would be exactly opposite only once (at exact 6 o'clock).
Thus, during the span of 12 hours, the two hands would be exactly opposite 11 times. Hence, in the span of 24 hours they would be exactly opposite 22 times.
ANSWER D
The answer is: D | D |
mathematics | If six persons sit in a row, then the probability that three particular persons are always together is | [
"1/5",
"1/8",
"1/5",
"1/3",
"1/1"
]
| Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability = 3!4!/6! = 1/5.Answer: C
The answer is: C | C |
mathematics | I. a3 - 305 = 207,
II. b2 - 72 = -8 to solve both the equations to find the values of a and b? | [
"a > b",
"a ≥ b",
"a < b",
"a ≤ b",
"a = b or the relationship between a and b cannot be established."
]
| a3 = 512 => a = 8
b2 = 64 => b = ± 8
a ≥ b
ANSWER:B
The answer is: B | B |
mathematics | The average of first 14 even numbers is? | [
"10",
"11",
"12",
"13",
"15"
]
| Sum of 14 even numbers = 14 * 15 = 210
Average =210/14= 15
ANSWER:E
The answer is: E | E |
mathematics | A shopkeeper sold an article for Rs 2552.36. Approximately what was his profit percent if the cost price of the article was Rs 2400 | [
"4%",
"5%",
"6%",
"7%",
"8%"
]
| Explanation:
Gain % = (152.36*100/2400) = 6.34 % = 6% approx
Option C
The answer is: C | C |
mathematics | If TEAR is coded as 4657 and BOX is coded as 125. How is BETA coded? | [
"1465",
"1645",
"1654",
"1456",
"1546"
]
| e=6 t-4 a-5 from the code TEAR, b-1 from the code BOX, ANSWER:B
The answer is: B | B |
mathematics | If a train, travelling at a speed of 90 kmph, crosses a pole in 4 sec, then the length of train is? | [
"281",
"125",
"288",
"100",
"121"
]
| D = 90 * 5/18 * 4
= 100 m
Answer: D
The answer is: D | D |
mathematics | The distance between Delhi and Mathura is 155 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? | [
"10.50 a.m.",
"11.00 a.m.",
"10.30 a.m.",
"11.40 a.m.",
"1.40 a.m."
]
| D = 155 – 20 = 135
RS = 20 + 25 = 45
T = 135/45 = 3 hours
8 a.m. + 3 hrs = 11.00 a.m.
ANSWER:B
The answer is: B | B |
mathematics | If a light flashes every 10 seconds, how many times will it flash in 2/3 of an hour? | [
"152",
"241",
"345",
"451",
"542"
]
| There are 60 minutes in an hour.
In 2/3 of an hour there are (60 * 2/3) minutes = 40minutes.
In 2/3 of an hour there are (60 * 40) seconds = 2400 seconds.
Light flashed for every 10 seconds.
In 2400 seconds 2400/10 = 240 times.
The count start after the first flash, the light will flashes 241 times in 2/3 of an hour.
Answer:B
The answer is: B | B |
mathematics | Three positive integers a, b, and c are such that their average is 18 and a ≤ b ≤ c. If the median is (a + 11), what is the least possible value of c? | [
"21",
"23",
"25",
"27",
"29"
]
| Solution:
We know that the average value is 18 therefore (a+b+c)/3 = 18
so a+b+c = 54
and b = a + 11
therefore a + (a + 11) + c = 54
The least value of c is when c = b
so take c = a + 11
hence, a + (a + 11) + (a + 11) = 54
i.e., a = 32/3 a non integer therefore c is not equal to b
so take c = b+1 therefore c = a+12
a + (a + 11) + (a + 12) = 54
i.e., a= 31/3 again a non integer therefore c is not equal to b+1
next take c= b+2 therefore c = a+13
a + (a + 11) + (a + 13) = 54
i.e., a=30/3 = 10
hence, a = 10, b = 21, and c = 23
Answer: B
The answer is: B | B |
mathematics | A 40 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume? | [
"810",
"12",
"13",
"14",
"16"
]
| Amount of salt = 4.0
Assume x gallons of water are added.
4.0 / 40 + x = 8/100
400 = 8x + 320
8x = 80
x = 10
Correct Option: A
The answer is: A | A |
mathematics | Insert the missing number
100,91,....,76,70 | [
"82",
"83",
"84",
"81",
"80"
]
| Missing number: 83
Answer: B
The answer is: B | B |
mathematics | If Rs. 762 be divided into three parts, proportional to 1/2:2/3:3/4, then the first part is? | [
"A)426",
"B)526",
"C)207",
"D)199",
"E)297"
]
| Given ratio
= 1/2:2/3:3/4 = 6:8:9
1st part = 762 * 6/23
= Rs. 199.
Answer:D
The answer is: D | D |
mathematics | In what time will a train 100 meters long cross an electric pole, if its speed is 126 km/hr | [
"8.5 seconds",
"2.86 seconds",
"3.5 seconds",
"2.5 seconds",
"2.6 seconds"
]
| First convert speed into m/sec
Speed = 126*(5/18) = 35 m/sec
Time = Distance/speed
= 100/35 = 2.86 seconds
Answer: B
The answer is: B | B |
mathematics | The average of 7 numbers is 15. If each number be multiplied by 5. Find the average of new set of numbers? | [
"A)110",
"B)122",
"C)90",
"D)85",
"E)75"
]
| Explanation:
Average of new numbers = 15 * 5 = 75
Answer: Option E
The answer is: E | E |
mathematics | The radius of a cylinder is 12 m, height 21 m. the lateral surface area of the cylinder is: | [
"1584",
"1854",
"1458",
"1485",
"None of them"
]
| Lateral surface area = 2πrh
= 2 × 22/7 × 12 × 21
= 44 × 36
= 1584 m(power2)
Answer is A.
The answer is: A | A |
mathematics | There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 28 possible combinations in which Michael is not selected, what is the value of n? | [
"7",
"8",
"9",
"10",
"11"
]
| The combinations of two people, in which Michael was not selected = 28
The number of ways two people can be selected from m people = m*(m-1)/2
Let m be the number of people excluding Michael.
Then m*(m-1) = 56 = 8*7
Thus, n = m + 1(Michael) = 9
The answer is C.
The answer is: C | C |
mathematics | A tradesman fixed his selling price of goods at 30% above the cost price. He sells half the stock at this price, one-quarter of his stock at a discount of 15% on the original selling price and rest at a discount of 30% on the original selling price. Find the gain percentage altogether? | [
"14.875%",
"15.375%",
"15.575%",
"16.375%",
"16.5%"
]
| Solution: Let CP = 100; then, marked price=130;
Now,
revenue = [(1/2)*130+(1/4)*0.85*130+(1/4)*0.7*130]
= 65+27.65+22.5 = 115.4;
% profit = 15.4*100/100 = 15.4%.
Answer: Option B
The answer is: B | B |
mathematics | During a special promotion, a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons. If Kim purchased 20 gallons of gas, and Isabella purchased 25 gallons of gas, then Isabella‟s total per-gallon discount is what percent of Kim‟s total per-gallon discount? | [
"80%",
"107%",
"116.7%",
"120%",
"140%"
]
| Kim purchased 20 gallons of gas. She paid for 5 + 0.9*15 = 18.5 gallons, so the overall discount she got was 1.5/20 = 7.5%.
Isabella purchased 25 gallons of gas. She paid for 5 + 0.9*20 = 23 gallons, so the overall discount she got was .5/25 = 8%.
8 is 8/7.5*100 = 107% of 7.5.
Answer: B.
The answer is: B | B |
mathematics | The average age 8 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number? | [
"12 years",
"14 years",
"18 years",
"16 years",
"26 years"
]
| 8 * 2 = 16 years
ANSWER:D
The answer is: D | D |
mathematics | By travelling at 50 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time? | [
"23 kmph",
"24 kmph",
"25 kmph",
"26 kmph",
"27 kmph"
]
| Let the time taken to reach the destination be 3x hours. Total distance = 50 * 3x = 150x km
He covered 2/3 * 150x = 100x km in 1/3 * 3x = x hours So, the remaining 50x km, he has to cover in 2x hours. Required speed = 50x/2x
=25 kmph.
Answer: C
The answer is: C | C |
mathematics | In how many different number of ways 4 man and 3 woman can sit on a bench such that girls always sit together. | [
"700",
"720",
"730",
"750",
"770"
]
| Option 'B'
The answer is: B | B |
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